Two-terminal band-pass coupling system



July 25, 1939.

H. A. WHEELER TWO-TERMINAL BAND-PASS COUPLING SYSTEM Filed April 22, 1938 217 Frequency H o q A2232 3:325: 2523- O FIG.3.

FIG.5

FIG.4.

FIG.6.

, FIG.7.

INVENTOR yRoLD A.WHEELER BY FIG.8.

ATTORN EY mated July25,-1o3o 2,167,137

UNITED STATES. PATENT OFF-ICE TWO-TERMINAL BAND-PASS COUPLING SYSTEM Harold A. Wheeler, Great Neck, N. Y., assignor to Hazeltlne Corporation, a corporation of Delaware Application April 22, 1938, Serial No. 203,598

8 Claims. (Cl. us-44) This invention relates generally to band-pass the filter are so proportioned relative to the coupling system and particularly to two-terminal capacitance associated with the terminals and coupling systems including a pair of terminals the operating frequency range that the impedance between which there is substantial capacitance across the terminals is substantially uniform over and between which it is desired to build up an the range and substantially the maximum that 5 impedance which is the maximum that can be can be maintained thereacross over the range.

maintained 'therebetween and which is substan- Other modifications and applications of the tially uniform over a wide band or wide bands of dead-end filter of the present invention are defrequencies, scribed and claimed in applicant's copending ap- 10 In many coupling systems it is desirable to plications Serial No. 203,595, Serial No. 203,596, 10 build up a substantially uniform impedance havand Serial No. 203,5'9'l, filed concurrently with ing the largest possible value over a wide band the present application while a general circuit of frequencies between terminals across which arrangement for maintaining uniform impedance there is substantial capacitance. For example, over a wide range of frequencies across a pair of in the design of band-pass vacuum-tube ampliterminals having inherent reactance associated ll flers to pass a wide band of frequencies, it is detherewith and tending to limit the response of sirable to build up across the inherent capacithe system over such range is disclosed and tance of the tube circuits to be coupled the maxbroadly claimed in applicant's copending appliimum impedance that can be maintained subcation Serial No. 161,017, filed August 26, 193'7,

stantially uniform over the operating frequency all assigned to the same assignee as the present band of the amplifier. Such impedance characapplication. teristics are procured in the coupling systems of The novel features believed to be characteristhe amplifier and the maximum value of the imtic of the invention are set forth with particupedance which can be maintained over a given larity in the appended claims. The invention itfrequency band is limited by the inherent capaciself, however, both as to its organization and g5 tance of the tube circuits to be coupled. Prior method of operation, together with further obart circuit arrangements designed for this purjects and advantages thereof, will best be unpose have fallen far short of the desired results. derstood by reference to the specification taken It is an object-of the invention, therefore, to in connection with the accompanying drawing,

provide a band-pass coupling system comprising in which Fig. 1 is a simplified or equivalent cir- 30 a pair of terminals between which there is subcult diagram of a band-pass filter embodying the stantial capacitance wherein 'a maximum mean invention, in order to explain the general theory value of impedance is maintained between the of the invention; Fig. 2 is a graph illustrating terminals of the coupling system over a wide certain of the operating characteristics of the band of frequencies. circuit of Fig. 1; and Figs. 3-8, inclusive, are cir; 35

It is another object of the invention to procult diagrams illustrating difierent embodiments vide a band-pass coupling system suitable for .of two-terminal band-pass coupling systems inuse between two successive tubes of a vacuumcorporating the invention. tube amplifier and having maximum impedance The principles of the theoretical relations unover a. wide frequency band. I derlying the invention are described most simply 40 In accordance with the invention, the bandby reference to a nondissipative wave filter of the .pass two-terminal signal-translating system for constant-k type. This filter may be assumed to operation over a wide range of frequencies comhave an infinite number of sections or to be ter-' prises substantial capacitance across its termiminated with its iterative impedance to give the nals tending to limit the response of the system same effect. The input impedance of. such a 111- over its range. A dead-end filter is coupled to ter is uniform .over the pass hands if the input the terminals having a predetermined image imtermination is full-series or full-shunt as dispedance over its range, the filter comprising only tinguished from the usual mid-series or mida part of the capacitance associated with the tershunt. The input impedance is the iterative imminals as a terminal mid-shunt element. A pedance measuredin series with a full-series arm 50 terminating resistor is provided for the dead end or in parallel with a full-shunt arm, as distinof the filter, the filter comprising an impedance guished from the conventional image impedance termination proportioned substantially to match measured at mid-series or mid-shunt. This inthe image impedance of'the filter with the reput impedance may be regarded as a two-tersistor over the range. The reactive constants of mine] coupling impedance, the remainder of the quency bands of total width An. In the case of filter serving merely as a dead-end sup lementary network utilized to secure the desired uniform impedance.

Any such filter of finite total band width can be arranged to include directly across its fullshunt arm, acapacitance of the value in which n is the mid-band image impedanee and A0 is 21 times the total width of the pass bands. The uniform full-shunt iterative impedance across the capacltance C has the magnitilde R=2/C'Au (2) This relationship expresses the theoretically maximum value of impedance that can be maintained across the capacitance C, throughout free a simple low-pass filter, the value of R is twice the reactance of the capacitance C at the cutoff frequency.

The reciprocal problem of building up impedance across a shunt capacitance is building up the admittance through an inductance. A filter can be arranged to include directly in series with all the other elements of its series arm, an inductance of the value The uniform full-series iterative gimpedance through the inductance L has the magnitude R'=LAn/2 (4) This relationship expresses the theoretically minimum value of impedance that can be maintained through an inductance L over the frequency bands of total width Au. In the case of a simple low-pass filter, this value is half the reactance of inductance L at the cutoff frequency. The specification will not be generalized to include derivations of expressions relating to maintaining a given value of impedance through an inductance,

because all the relations hereinafter given can be applied to this problem by the analogy which appears in the preceding formulae.

The image impedance of a filter of the type h under discussion is' purely resistive in the pass bands, though not uniform. On the other hand, the uniform iterative impedance has a substantial phase angle which is a lagging phase angle as referred to the impedance across a capacitance or the admittance throughan inductance. The phase characteristic is that of a half-section of a constant-k filter. A more general analysis is given hereinafter with reference to a simple lowpass filter, without any loss of generality in the foregoing concepts; Referring now to the drawing, Fig. 1 shows the basic filter circuit in simplified .form, the filter, per se, being represented schematically at I and having input terminals I and output terminals 9. The input termination C111 of filter I is a mid-shunt element and the input image impedance Z1 follows the constant-k characteristic. The output termination of filter I is either mid-series or mid-shunt and its image impedance Z1 preferably follows an m-derived characteristic to match closely the output load resistance Re. In developing the theoretical relations, this impedance matching is assumed to be exact in the pass bands, since any required degree of approximation is possible by means of multiple m-derivations. 1 For the sake of generality and clarity, the total capacitance Co'BCl'OSS the input terminals l may have any value and is divided in two parts,

a,1ev,1sr v 7 C111 comprising the mid-shunt capacitance termination of the filter, and C11 the external added capacitance, thus, only a part of the total capacitance across the terminals I is includedin the filter as a mid-shunt element. The input imped- Cm=mlRooc (5) in which we is 21 fe, where je is the cutoff frequency of the low-pass filter. The external shunt capaci V tance'on'can have any value as determined by the choice of the parameter n in the formula,

I Ca=1l/Ro0cf Therefore, the total shunt capacitance is c.=c,.+c..=(m+n) we. ('1) The factor (m+n) may have any positive value.

One of the parts may be negative, since the do not have to exist separately. Negative C11 merely means that the total capacitance Ce is less than the mid-shunt capacitance C111 of the filter. Equation 7 may also be written as oe=(m+n)/C1 Re (s) Ro=(m+1l)/cowc (9) ReCwe=m+n (10) The image impedance Z1 depends only on Re and we, not on C111 and m, because it always has the constant-k characteristic The image impedance is resistive in the pass band, capacitive'in the atenuation band, and infinite at the cutoff frequency. It is convenient to use the parameter x=w/ oe to denote the relative frequency in subsequent expressions. The

relative impedance of C11 and Z1 in parallel is e J i-i-j e /1x'+jxn This formula has a discontinuity at the cutoff frequency (;c=1), where the Z1 term of the denominator changes from real to imaginary. It

is seen that the form of the impedance characteristic depends only on vn=1atcm (is from Equation 6, and does not depend on m=Rocnwc (14) from Equation 5.

In the pass band ('a: l) -Z/Re is'complex and its magnitude is /1 +x '(n'l) If n=1, this is constant (unity). For-greater values of n, it has the form of a simple resistor and capacitor in parallel, though the phase angle phase angle aqua- This is the same as the formula for a half-section m-type filter except that the m of the filter is replaced by the parameter 1: which determines the relative value of Ca. If n=1, it simplifies to It has a lagging phase angle, b=a'/2. These.

- b=sina: (l7) In the attenuation band (a: 1) Z/Ro is imaginary and its magnitude is characteristics'cannot be realized exactly because the output image impedance Zr cannot match R0 outside the pass band. As theattenuation increases, this failure has less efi'ect on the input impedance. Therefore, any degree of approximation to the theoretical characteristics outside the pass band can be realized with a sufilcient number of sections designed to secure adequate attenuation. k

Fig. 2 shows the theoretical impedance characteristics for various values of the parameter n between -1 and +4. It is noted that the values 1-1 yield uniform impedance in the pass hand. If the filter has a constant-k whole section on the input side, so that m=1, the values +1 and l for n correspond, respectively, to full-shunt and full-series termination. In the former case, the addition of on doubles the mid-shunt element, while in the latter case it cancels the midshunt "element. The sign of the parameter n does not afiect the magnitude of the impedance in the pass band, but it does determine the sign of the phase angle.

Since only positive self-reactance elements can be realized in a passive network, the value of m in the end half-section of a filter must be between 0 and +1. Since m+n must be positive, the value of 1: must be between 1 and Negative values of 11 make the impedance infinite at the frequency quency of infinite impedance. ,If n=:1 in Equation 20, the product is unity so the impedances are mutually reciprocal.

Any of the impedance characteristics of Fig. 2 are theoretically obtainable across a maximum value of total shunt capacitance if m=1, n having the value identified with the characteristic curve. If m is less than one, the total capacitance directly across the input terminals is less by the amount added indirectly across the input terminals through the other arms of the filter. Therefore, a uniform impedance equal to R0 in I 3 the pass band is obtainable across a maximum total capacitance, directly and indirectly in shunt. whose value is computed by letting 1n=n=1z Co=2/Rm (21) which corresponds to Equation 1. Any change of the total capacitance, by changing the value of n, causes an inverse change of the average impedance in the pass band, although its value R0 .at zero frequency remains the same.

In the pass band, the impedance near the cutofi frequency is determined mainly by the value of n, that is, by the external shunt capacitance Cn. The image impedance Z1 having less efiect, the tolerance of mismatching between Z1 and R0 at the far end of the filter becomes greater. Also this tolerance increases with n. The number of sections in the filter aifects the number of be supplemented by parallel branches to form an impedance network of the form required in a constant-k shunt arm to give the required pass bands. Cn also may be supplemented, and in this case the inside and outside shunt arms can still be merged into one. The generalized relation corresponding to Equation 10 is RoCoAw=m+n (22) in which Aw is the total width of the pass bands. Uniform-impedance of magnitude R0 is secured in all pass hands if n=l. It is secured with maximum shunt capacitance if also m=1. This expression, for uniform impedance, may be designated as the figure of merit of any particular network, its maximumvalue being two.

Fig. 3 shows the application of the general concepts to a simple band-pass filter. 'Itis assumed that the impedance level is the same at both ends of the filter, otherwise both Z1 and R0 are multiplied by a factor of transformation. The values of. shunt capacitance are in which 01 and us are 21rtimes the cutoff frequencies. The basic relation of Equation 22 is then Roco(w2c)1)=m+fl (24) Parallel inductances La and Lb are provided to resonate with Cm and Cu, respectively, at the mean resonant frequency of the band in order to provide the desired band-pass characteristics. The band-pass filter of Fig. 3 comprises, in the order named, a parallel-resonant circuit com-. prising inductance Lb and capacitance Cn, a constant-Ic half-section of whichthe parallel-resonant elements Cm and La comprise a mid-shunt element, and a terminating resistor R0 the resistance of which approximately matches the image impedance of the filter over the pass band.

Figs. 4-8, inclusive, relate to filters comprising additional or modified sections which are particularly useful practical embodiments of the invention. a

The filter of Fig. 4 comprises, in the order named, a parallel-resonant circuit Lb, Cn, a

modified constant-k full section k of which elements Cm and La comprise a mid-shunt eleance of' which approximately matches the image impedance of the filter over the pass band.

The filter of Fig. 5 comprises, inthe order named, a parallel-connected inductance Ia and capacitance C, an m-derived half-section of which the parallel connected inductance L. and

' capacitance Cm form a mid-shunt element, and a-terminating resistor Rs the resistance of which approximately matches the image imp i ce of the-filter over the pass band. i.

The filter of Fig. 6 comprises, in the order named, a parallel-connected inductance La and capacitance. On, a constant-k half-section ofwhich capacitance Cm and inductance La comprise the mid-shunt element, an m-derived halisection indicated as m in the drawing, and a' terminating resistor R0 -whlch very closely I matches the image impedance of the dead-end of the filter 'over the pass band. The circuitof Fig. 6a. is the full electrical equivalent of the circuit of Fig. 6 in which the inductive elements of Fig. 6 have been replaced by equivalenttransformers 2| and II, and in which elements Cu and Cm have been combined into the single element Co.

The circuit of Fig. '1 comprises, in the order named, a parallel resonant circuit Ls,- Ca, a modified constant-k filter section k of which capacitance Cm and inductance L. comprise a mid-shunt element, an m-derived half-section indicated as m on the drawing. and a terminating resistor R0 which very closely matches the image impedance of the dead end of the filter over the pass band.

The dead-end filter of the circuit of Fig. 8 is in all respects equivalent to that of Fig. 'l and is utilized as a band-pass coupling impedance between amplifier tubes II and Ii. Capacitance elements Cr\ and Ca are combined in the capacitance l2 shown in'dotted lines in the drawing. This capacitance II is'comprised mainly of the inherent output capacitance oi tube II and the input capacitance of tube ll. Trans Jrmers is provided for the input circuit of vacuum tube H. The other elements of the circuit of Fig. 8 are conventional and its operation will readily be understood from the description or the filter of the invention given above. it being understood that by utilizing the dead-end filter of the present invention, the presence of the shunt capacitance I! does not seriously reduce the response of the coupling system nor impair its uniformity over the pass band. On the contrary, there is built up across this capacitance a high impedance which is nearly uniform over the pass band, giving a correspondingly high and uniform response characteristic. V

In the design of the dead-end filters of the invention; the preferred value of m in the mderived sections is of the order oi. 0.6. Values of m between the limits of 0.5 to 0.! result in a matching of the image impedance of the mderived filter section with the terminating resistor. R0 at four points in a band-pass band. Filters having an m-derived termination with a value of m more than 0.! cannot match the terminal resistor R5 at more than two points in a pass band filter. Each additional m-derivation in the filter section included inthe filter termination makes it possible to match the image impedance with the terminal resistor at two addi- 'tional points in the pass band. re While there have been described what are at present considered to be the preferred embodiments of this invention. it will be obvious to those skilled in the art that various changes and modifications may be made therein without departing from the invention, and it is, therefore, aimed in the appended claims to cover all such changes and modifications as fall within the true spiritand scope of the invention.

What is claimed is: p ,1. A band-pass two-terminal signalsystem for operation over a wide range of fre quencies comprising substantial capacitance across said terminals tending to limit the response of said system over said range, a dead;-

end filter having a predetermined image imped-- ance over said range and coupled to said terminals, said'filter comprising only a part of said nslating capacitance as a terminal mid-shunt element, a 35 terminating resistor for the dead end of said filter, said filter comprising an impedance termination proportioned substantially to match the image impedance of said filter with said resistor.

over said range, the reactive'constants oi-said filter being so proportioned "relative to said capacitance and the operating frequency range that the impedance across said terminals is sub- -stantially uniform over said range and substantially the maximum that can be maintained thereacross over said range. U j

, 2.1 A'band-pass two-terminal signal-translating system for operation over a wide range of fre-, quencies comprising substantial capacitance across said terminals tending to limit'the response of said system over said range, a deadend filter having a predetermined image im-. pedance over said range and coupled to said terminals, said filter comprising only a part of said capacitance as a terminal mid-shunt element and an inductance in parallel with said capacitance efiectively providing a circuit resonant at the mean frequency of said band, a terminatins resistor for the dead end of said filter, said filter comprising an impedance termination proportioned substantially to match the image impede ance of said filter with said resistor over said range, the reactive constants of said filter being so proportioned relative to said capacitance and the operating frequency range that the impedance across said terminals is substantially uniform over said range and substantially the maximum thatcan be maintained thereacross over said range.

3. A band-pass two-terminal signal-translating system for operation over a wide range of frequencies comprising substantial capacitance across said terminals tending to limit the response of said system over said range, a dead-end filter having a predetermined impedance :over said range and coupled to said terminals, said. filter comprising only a part of said capacitance as a terminal mid-shunt element, a section of said filter having a uniform image impedance at one end and an image impedance substantially 10 saidsection. the reactive of. said 111151 I! quencies mum that can be' maintained thereacross over said range. k

4. A band-"pass two-terminal signal-translating system for operation over a wide range of frecomprising substantial capacitance across said terminals tending to limit the response of said system over said range, a dead-end filter having a predetermined image impedance over said range coupled to said terminals, said filter efiectively comprising only a part of said capacitance as a terminal mid-shunt element, a terminal resistor for said dead-end filter, said filter effectively including an impedance termination comprising a modified constant-k section including two parallel-resonant shunt arms with an inductance series arm interposed therebetween, said termination being coupled and proportioned substantially to match the image impedance of said filter with said resistor over said range, the reactive constants of said filter beingso proportioned relative to said capacitance and the oper ance over said range coupled to said terminals,

said filter comprising only a part of said capacitance and an inductance as a terminal midshunt element, and an impedance termination for said filter effectively comprising a parallel-resonant circuit as a shunt arm and a series-resonant circuit and a parallel resonant circuit coupled in.

parallel as a series arm, a terminal resistor for said impedance termination, said termination being coupled to the dead end of said filter and being proportioned substantially to match the image impedance of said filter with said resistor over said range, the reactive constants of said dead-end filter being so proportioned relative to said capacitance and the operating frequency range that the impedance across said terminals is substantially uniform over said range and substantially the maximum that can be mainage impedance over said range coupled, to said terminals, said filter effectively comprising only a part of said capacitance and an inductance in parallel therewith as a terminal mid-shunt element, an m-derived impedance termination effectively comprising a series-resonant series-arm being so proportioned relative to said capacitance k 5 and a shunt arm including a series-resonant circuit and a parallel-resonant circuit eifectiveb in series, a terminal resistor for said impedance termination, said termination being coupled to the dead end of said filter and being proportioned substantially to match the image impedance of said filter with said resistor over said range, the reactive constants of said dead-end filter being so proportioned relative to said capacitance andacross said terminals tending to limit the response of said 'system over said range, an impedance network having a predetermined imageimpedance over said range coupled to said terminals, said impedance network comprising a first-transformer having a primary winding tuned by a. portion of said capacitance, a second transformer having a primary and a tuned secondary windins, two condensers connected in series with the primary of said second transformer across the secondary winding of said first transformer, a'resistor coupled across the primary circuit of said second transformer andone of said two condensers, the reactive constants of said impedance network being so'proportioned relative to the value of said resistor, said capacitance, and the operating frequency range that the impedance across said terminals is substantially uniform over said range and substantially the maximum that can be maintained thereacross over said range.

8. A band-pass two-terminal signal-translating system for operation over a wide range of frequencies comprising substantial capacitance across said terminals tending to limit the rei sponse of said sysetm over said range, a deadend filter having a predetermined image impedance over said range coupled to said terminals, said filter efi'ectively comprising only a part of said capacitance and an inductance as a terminal mid-shunt element and a modified constant-k section including two parallel-resonant shunt arms and an inductive series arm, an m-derived impedance termination coupled to the dead end of saidfilter comprising a series arm including a series-resonant circuit and a parallel-resonant circuit connected in parallel, a terminal resistor, said impedance termination being coupled to the dead end 'of said filter and being proportioned substantially to match the image impedance of said filter with said resistor-over said range, the

reactive constants ofisaid dead-end filter being said range.

' HAROLD A. 

